|
Week 1 |
Function of a Complex
Variable |
|
Wednesday
Sep 23 |
Algebra, complex plane, Argand diagram, de Moivre’s theorem,
trigonometric series |
3
|
|
Friday
Sep 25 |
Analytic
functions, Cauchy-Riemann conditions, Riemann sheets, branch
cuts
|
24.1 - 24.6
|
|
|
|
|
Week 2 |
Function of a Complex
Variable |
|
Monday
Sep 28 |
Contour
integrals, Cauchy’s Theorem and integral formula,
Taylor expansion |
24.8 - 24.11
|
|
Wednesday
Sep 30 |
Analytic continuation, Laurent series, poles, calculus
of residues |
24.12
|
|
Friday
Oct 2 |
Contour
integration: Examples |
24.13
|
|
|
|
|
Week 3 |
Finite Dimensional
Vector Spaces |
|
Monday
Oct
5 |
Contour
integration with branch cuts |
24.13
|
|
Tuesday
Oct 6
X-Hr
12-12:50p |
Linear
vector spaces, algebra, linear independence, basis set,
transpose, inner product |
8.1
|
|
Wednesday
Oct
7 |
Matrix
operations, linear operators, classes of operators, examples
|
8.2-8.12
|
|
Friday
Oct
9 |
Eigenvectors/values, inequalities, Gram-Schmidt
orthogonalization |
8.13
|
|
|
|
|
Week 4 |
Finite Dimensional
Vector Spaces |
Monday
Oct 12 |
Unitary
operators, eigenvalues/vectors, diagonalization,
characteristic equation
|
8.13 - 8.14
|
|
Wednesday
Oct 14
|
Change of basis, orthogonal transformation, eigenproblems |
8.15 - 8.17
|
|
Friday
Oct 16 |
Systems of
linear differential equations |
8.18, 9.1
|
|
|
|
|
Week 5 |
Linear Differential
Equations |
|
Monday
Oct 19 |
Second order DEs, ordinary and singular points,
series
solution |
16.1
|
|
Wednesday
Oct 21 |
Series solution and Method of Frobenius |
16.2
|
|
Friday
Oct 23 |
Series expansion around a singular point, Bessel’s equation
and functions |
16.3
|
|
|
|
|
Week 6 |
Linear Differential
Equations |
|
Monday
Oct 26 |
Missing solutions, logarithmic solution |
16.4
|
|
Wednesday
Oct 28 |
Legendre's equation and polynomial solutions |
16.6
|
|
Friday
Oct 30 |
Nonhomogenous problem, families of ODES |
Notes
|
|
|
|
|
Week 7 |
Infinite Dimensional
Vector Space |
|
Monday
Nov 2 |
Hilbert space, self-adjoint operator, complete and
orthonormal sets |
17.1 - 17.2
|
|
Wednesday
Nov 4 |
Eigenfunction expansions |
|
|
Friday
Nov 6 |
Boundary value problems, Sturm-Liouville problem |
17.4
|
|
|
|
|
Week 8 |
Infinite Dimensional
Vector Spaces |
|
Monday
Nov 9 |
Green's
functions |
17.5 - 17.6
|
|
Wednesday
Nov 11 |
Gamma
function |
18, Notes
|
|
Friday
Nov 13 |
Hypergeometric and special functions |
18, Notes
|
|
|
|
|
Week 9 |
Integral Transforms |
|
Monday
Nov 16 |
Orthogonal
polynomials |
18, Notes
|
|
Wednesday
Nov 18 |
Fourier
transform, convolution, Parseval relation, uncertainty
principle |
13.1
|
|
Friday
Nov 20 |
Laplace
transform, an application leading to Abel’s integral
equation |
13.2
|
|
|
|
|
Week 10/11 |
Integral Transforms |
|
Monday
Nov 23 |
General
approach to the derivation of transform pairs |
Notes
|
|
Monday
Nov 30 |
Other transform pairs |
Notes
|
|
Wednesday
Dec 2 |
Applications |
|
